Pipes and Cisterns- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems on Pipes and Cisterns. Basic knowledge
regarding solving questions and problems on filling and emptying a tank with pipes in specific duration of time is important for various competitive exams like IBPS,
SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

Concept of Pipes and Cisterns/ Tanks:

A cistern is a water tank that has taps to fill or empty it.

Pipes can be used to fill or empty the tank.

Important Shortcuts and Formulae Regarding Pipes and Tanks

Case I: If a pipe can fill a tank in N hour then:

Part filled in 1 hour = 1/N

Case II: If a pipe can empty a tank in E hours

Part emptied in 1 hour = 1/E

Case III: If there are two pipes A and B and they can fill a tank in M and N hours respectively, both pipes opened simultaneously

Part filled in 1 hour = 1/M + 1/N

Time to fill tank= MN/(M+N) hours

Case IV: If a pipe can fill a tank in N hour and other pipe can empty it in E hour, on opening both pipes simultaneously:

Part filled in 1 hour = 1/N - 1/E (if N < E)

Part emptied in 1 hour = 1/E - 1/N (if E < N)

Time to fill the tank = EN/(E-N) (if N < E)

Time to empty the tank = EN/(N-E) (if E < N)

Below are some examples and problem solving tricks on Pipes and Cisterns

Example 1: Two pipes A and B can fill the tank in 2 and 3 hours respectively. If both pipes are used together, then how long will it take to fill the tank?Solution: Using formula above both pipes can fill the tank in 2*3/(2+3) = 6/5 hr = 1 1/5.

Example 2: A pipe can fill the tank in 2 hours and other pipe can empty itt in 3 hour. If both pipes are used together, then how long will it take to fill the tank?Solution: Using formula above time taken by both pipes to fill the tank is 2*3/(3-2) = 6 hrs

Example 3: Two pipes can fill a tank in 4 and 6 hours respectively while third pipe can empty it in 5 hours. If all three pipes are opened simultaneously in how much time will the tank be filled?Solution: Net part filled in 1 hour = 1/4 + 1/6 - 1/5 = 13/60
Hence total time to fill the tank = 60/13 = 4 8/13 hrs.

Example 4: Two pipes can fill a tank in 12 hours and 15 hours respectively. There is also a waste pipe which can empty the tank. When all three pipes are opened they emptied the tank in 20 minutes. How long will waste pipe take to empty the tank alone?Solution: Let third pipe takes X hours to empty the tank.
Tank emptied in 1 hr = 1/20 = 1/12 + 1/15 - 1/X
=>1/X = 1/12 + 1/15 - 1/20 = 1/10
=> X = 10 hours.

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